This seems to not support the Tado AC and I get the impression it does not claim to do so. I also get the impression HomeAssistant does not support using Tado to control hot water heating either and therefore is limited to just central heating control.

It is however possible in theory to connect Tado devices to HomeAsisstant in at least two other ways.

Via an MQTT broker, this allows HomeAssistant to talk via MQTT to another smart home platform e.g. Samsung Smartthings and share devices with that other platform